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Closed expression of the interaction kernel in the Bethe-Salpeter equation for quark-antiqu

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a rXiv:h ep-th/02226v224O ct25Closed expression of the interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states Jun-Chen Su .Center for Theoretical Physics,Physics College,Jilin University,Changchun 130023,People’s Republic of China The interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states is derived from QCD in the general case where the quark and the antiquark can be of different flavors or the same flavor.The kernel is derived with the aid of the Bethe-Salpeter equations satisfied by the quark-antiquark four-point Green function.The latter equations are established based on the equations of motion obeyed by the quark and antiquark propagators,the quark-antiquark four-point Green function and some other kinds of Green functions in which the gluon field is involved.The interaction kernel derived is given a closed and explicit expression.Since the kernel is represented in terms of only a few-types of Green functions,it is not only convenient for perturbative calculations,but also suitable for nonperturbative investigations.PACS:11.10St,12.38.Aw, Key words:Bethe-Salpeter equation,interaction kernel,quark-antiquark bound state.I.INTRODUCTION The Bethe-Salpeter (B-S)equation which was established early in Refs.[1,2]is recognized as a rigorous approach to the relativistic bound state problem and has extensively been investigated in the period of more than half century [3-21].The distinctive features of the equation are:(1)The equation is derived from quantum field theory and hence set up on the firm dynamical basis;(2)The interaction kernel in the equation contains all the interactions taking place in the bound states and therefore the equation provides a possibility of exactly solving the problem of relativistic bound states;(3)The equation is elegantly formulated in a manifestly Lorentz-covariant form in the Minkowski space which allows us to discuss the equation in any coordinate frame.However,there are tremendous difficulties in practical applications of the equation.One of the difficulties arises from the fact that the kernel in the equation was not given a closed form in the ually,the kernel is defined as a sum of all B-S irreducible (or say,two-particle-irreducible)graphs.According to this definition,the kernel can only be calculated by the perturbation method.In practical applications,the perturbation series of the kernel has to be truncated in a ladder approximation.The ladder approximation has been proved to be successful in QED for studying the bound states formed by the electromagnetic interaction [22-26].Nevertheless,it is not feasible in QCD for exploring multi-quark bound states because the confining force which must be taken into account in this case could not follow from a perturbative calculation.It was remarked in Ref.[27]that ”The approach using the Bethe-Salpeter equation has not led to a real breakthrough in our understanding of quark-quark force”.The reason is mainly due to that”we have no method for computing the kernel of the B-S equation”because we have not known the closed expression of the kernel which can be used to evaluate the confining force.In the previous application of the B-S equation to investigate the hadron structure,a phenomenological confining potential is necessarily introduced and added to the one-gluonexchange kernel so as to obtain reasonable theoretical results [27-29].The confining potential was originally proposed from a nonperturbative computation,for example,the lattice gauge calculation for a special Wilson loop [30-33].Since the B-S equation is an exact formalism for bound states and the B-S kernel contains all the interactions responsible for the formation of the bound states,the B-S kernel is supposed to be the most suitable starting point of examining the quark confinement.The question now is concentrated on whether a closed expression of the B-S kernel exists and can be derived?The aim of this paper is to give a definite answer to this question.It will be shown that opposite to the conventional concept that ”The kernel K can not be given in a closed form expression”[34],a closed expression of the B-S kernel for quark-antiquark bound states will perfectly be derived in this paper.The method of deriving the expression of the kernel is usage of various equations of motion satisfied by the qAppendix,the equations of motion satisfied by some Green functions which are necessary to use in the derivation of the B-S kernel are derived.II.DEFINITION OF THE B-S KERNELTo derive the B-S interaction kernel appearing in the B-S equation for qq four-point Green function.For the qψρ(y1)ψ(x)andψT(x),S∗F(y1−y2)ρσ(2.4) whereG(x1,x2;y1,y2)αβρσ= 0+ T{ψα(x1)ψcβ(x2)ψcσ(y2)} 0− (2.5) is the conventional qi 0+ T[ψα(x1)ψcβ(x2)] 0−=S F(x1−x2)αγ(C−1)γβ=S c F(x2−x1)βλCλα(2.6)andi 0+ T{ψcσ(y2)} 0−=CστS F(y2−y1)τρ=(C−1)ρδS c F(y1−y2)δσ(2.7) in whichS F(x1−x2)αγ=1ψγ(x2)] 0− (2.8)andS c F(y1−y2)δσ=1ψcσ(y2)} 0− (2.9)are the ordinary quark and antiquark propagators respectively[5].It is clear that the propagators defined in Eqs.(2.6)and(2.7)are nonzero only for such a quark and an antiquark that they are of the sameflavor.For the quark and antiquark of differentflavors,the Green function defined in Eq.(2.1)is reduced to the conventional form shown in Eq.(2.5)since the second term on the right hand side(RHS)of Eq.(2.4)vanishes.In the case of the quark and antiquark of the sameflavor,the normal product in Eq.(2.1)plays a role of excluding the contraction between the quarkfield and the antiquark one from the Green function.Physically,this avoids the qψ(x)to represent the antiquarkfield in this paper has an advantage that the antiquarkfield would behave as a quark one in the B-S equation so that thequark-antiquark equation formally is the same as the corresponding two-quark equation in the case that the quark and antiquark have differentflavors.Now let us proceed to the derivation of the B-S equation for the qi 0+ T[A aµ(x1)ψγ(x1)Γbν)βλΛc bν(x2|x2,y2)λσ(2.15) hereT b(2.16) withi 0+T[A bν(x2)ψcλ(x2)i0+|T[A aµ(x i)...A bν(x j)A cκ(y k)...A dθ(y l)ψα(x1)i0+|T[A aµ(x i)...A bν(x j)A cκ(y k)...A dθ(y l)ψcβ(x2)i 0+|T[A aµ(x i)...A bν(x j)A cκ(y k)...A dθ(y l)ψα(x1)ψcβ(x2)]|0−(2.20)i 0+|T[A aµ(x i)...A bν(x j)A cκ(y k)...A dθ(y l)ψcσ(y2)]|0−(2.21)G a...bc...dµ...νκ...θ(x i,...,x j;y k,...,y l|x1,x2;y1,y2)αβρσ= 0+|T[A aµ(x i)...A bν(x j)A cκ(y k)...A dθ(y l)ψα(x1)ψcβ(x2)ψcσ(y2)]|0−(2.22)andG a...bc...dµ...νκ...θ(x i,...,x j;y k,...,y l|x1,x2;y1,y2)αβρσ= 0+|T{N[A aµ(x i)...A bν(x j)ψα(x1)ψcβ(x2)]N[ψcσ(y2)A cκ(y k)...A dθ(y l)]}|0−(2.23)where i,j.k,l=1,2.The normal products in Eq.(2.23)are defined in the same way as that in Eq.(2.3).Hereafter, we no longer write individual representations of the Green functions encountered in later derivations.They can be read offfrom the above expressions.According to the derivations given in the appendices,we can write from Eqs.(A24)and(B4)the equations of motion obeyed by the Green function defined in Eq.(2.5)[5][(i∂x1−m1+Σ)G]αβρσ(x1,x2;y1,y2)=δαρδ4(x1−y1)S c F(x2−y2)βσ+Cαβδ4(x1−x2)S∗F(y1−y2)ρσ−(S∗F(y1−y2)ρσ(2.26)where i=1,2.On substituting the definitions in Eqs.(2.4)and(2.26)into Eqs.(2.24)and(2.25),employing the equations in Eqs.(2.10)and(2.14)and the relations in Eqs.(2.6),(2.7),(2.11)and(2.15),it is not difficult to derive the following equations[(i∂x1−m1+Σ)G]αβρσ(x1,x2;y1,y2)=δαρδ4(x1−y1)S c F(x2−y2)βσ−(Γaµ)αγG aµ(x1|x1,x2;y1,y2)γβρσ+ d4z1Σ(x1,z1)αγG(z1,x2;y1,y2)γβρσ(2.27) and[(i∂x2−m2+Σc)G]αβρσ(x1,x2;y1,y2)=δβσδ4(x2−y2)S F(x1−y1)αρ−(Γbν)βλ[(i∂x1−m1+Σ)G bν]αλρσ(x2|x1,x2;y1,y2)+ d4z2Σc(x2,z2)βλ[(i∂x1−m1+Σ)G]αλρσ(x1,z2;y1,y2).(2.29)Thefirst and third terms in the above can directly be evaluated by employing Eqs.(2.10)and(2.27).To compute the second term,wefirst write down the equation of motion for the Green function G bν(x2|x1,x2;y1,y2)which is given by supplementing the self-energy-related term to the both sides of Eq.(A25)[(i∂x1−m1+Σ)G bν]αλρσ(x2|x1,x2;y1,y2)=δαρδ4(x1−y1)Λc bν(x2|x2,y2)λσ+Cαλδ4(x1−x2)Λ∗bν(x2|y1,y2)ρσand G abµν(x1,x2|x1,x2;y1,y2)γλρσare the Green functions which can be read offfrom Eqs.(2.19),(2.21)and(2.22)respectively.According to the relation shown in Eq.(2.26)and the following relation which follows from Eq.(2.23)G abµν(x1,x2|x1,x2;y1,y2)αβρσ=G abµν(x1,x2|x1,x2;y1,y2)αβρσ+Λ∗abµν(x1,x2|x1,x2)αβΛ∗bν(x2|y1,y2)ρσ−(Γaµ)αγG abµν(x1,x2|x1,x2;y1,y2)γλρσ+ d4z1Σ(x1,z1)αγG bν(x2|z1,x2;y1,y2)γλρσ.(2.33) Upon inserting Eqs.(2.10),(2.27)and(2.33)into Eq.(2.29),we arrive at[(i∂x1−m1+Σ)(i∂x2−m2+Σc)G]αβρσ(x1,x2;y1,y2)=δαρδβσδ4(x1−y1)δ4(x2−y2)+H1(x1,x2;y1,y2)αβρσ(2.34) whereH1(x1,x2;y1,y2)αβρσ=5i=1H(i)1(x1,x2;y1,y2)αβρσ(2.35)in whichH(1)1(x1,x2;y1,y2)αβρσ=−(Γaµ)αγ d4z2Σc(x2,z2)βλG aµ(x1|x1,z2;y1,y2)γλρσ,(2.36)H(2)1(x1,x2;y1,y2)αβρσ=−(Γbν)βλG abµν(x1,x2|x1,x2;y1,y2)γλρσ,(2.38)H(4)1(x1,x2;y1,y2)αβρσ=δ4(x1−x2)(Λ∗bν(x2|y1,y2)ρσ(2.39) andH(5)1(x1,x2;y1,y2)αβρσ= d4z1d4z2Σ(x1,z1)αγΣc(x2,z2)βλG(z1,z2;y1,y2)γλρσ.(2.40)From perturbative calculations or irreducible decompositions of the Green functions[1-5,21],it may be found that the function H1(x1,x2;y1,y2)is B-S reducible and can be written in the formH 1(x 1,x 2;y 1,y 2)αβρσ= d 4z 1d 4z 2K (x 1,x 2;z 1,z 2)αβγλG (z 1,z 2;y 1,y 2)γλρσ(2.41)where K (x 1,x 2;z 1,z 2)is precisely the B-S irreducible kernel.With the above expression for the function H 1(x 1,x 2;y 1,y 2),the equation in Eq.(2.34)can be expressed in a closed form[(i∂x 1−m 1+Σ)(i∂x 2−m 2+Σc )G ]αβρσ(x 1,x 2;y 1,y 2)=δαρδβσδ4(x 1−y 1)δ4(x 2−y 2)+ d 4z 1d 4z 2K (x 1,x 2;z 1,z 2)αβγλG (z 1,z 2;y 1,y 2)γλρσ.(2.42)This just is the B-S equation satisfied by the Green function G (x 1,x 2;y 1,y 2).By making use of the Lehmann rep-resentation of the Green function G (x 1,x 2;y 1,y 2)or the well-known procedure proposed by Gell-Mann and Low [2],one may readily derive from Eq.(2.42)the B-S equation satisfied by B-S amplitudes describing the qq bound state and ςmarks the otherquantum numbers of the state.The above equation can be written in the form of an integral equation when we operate on the both sides of the above equation with (i∂x 1−m 1+Σ)−1(i∂x 2−m 2+Σc )−1[1-5]χP ς(x 1,x 2)= d 4z 1d 4z 2d 4y 1d 4y 2S F (x 1−z 1)S c F (x 2−z 2)K (z 1,z 2;y 1,y 2)χP ς(y 1,y 2)(2.45)III.DERIV ATION OF THE B-S KERNELBeyond the perturbation method,the B-S kernel may be derived by starting from its definition shown in Eq.(2.41).One method of the derivation is usage of the technique of irreducible decomposition of Green functions.By this method,once the one and two-particle-irreducible decompositions of the Green functions contained in the function H 1(x 1,x 2;y 1,y 2)are completed,it can be found that the function H 1(x 1,x 2;y 1,y 2)can really be represented in the form as written in Eq.(2.41)and,at the same time,the kernel will be explicitly worked out.Nevertheless,the expression of the kernel given in this way is much complicated (We leave the detailed discussions in the future).Another method of deriving the kernel is to use B-S equations which describe variations of the Green functions involved in the function H 1(x 1,x 2;y 1,y 2)with the coordinates y 1and y 2.In this paper,we adopt the latter method and describe the procedure of the derivation in this section.Let us operate on the both sides of Eq.(2.41)from the right with the operator (i ←−∂y 1+m 1−Σ)(i ←−∂y 2+m 2−Σc )such thatd 4z 1d 4z 2K (x 1,x 2;z 1,z 2)αβγλ[G (i ←−∂y 1+m 1−Σ)(i ←−∂y 2+m 2−Σc )]γλρσ(z 1,z 2;y 1,y 2)=Q (x 1,x 2;y 1,y 2)αβρσ(3.1)whereQ (x 1,x 2;y 1,y 2)αβρσ=[H 1(i ←−∂y 1+m 1−Σ)(i ←−∂y 2+m 2−Σc )]αβρσ(x 1,x 2;y 1,y 2).(3.2)As seen from Eqs.(3.1)and (3.2),to derive the B-S kernel,it is necessary to use the B-S equations with re-spect to y 1and y 2for the Green function G (x 1,x 2;y 1,y 2)and the other Green functions appearing in the function H 1(x 1,x 2;y 1,y 2).Analogous to the procedure stated in the preceding section,the above-mentioned B-S equations can be derived with the aid of equations of motion with respect to y 1and y 2for those Green functions.First,we show the equations of motion obeyed by the quark and antiquark propagators[S F (i ←−∂y 1+m 1−Σ)]αρ(x 1,y 1)=−δαρδ4(x 1−y 1)(3.3)and[S c F (i ←−∂y 2+m 2−Σc )]βσ(x 2,y 2)=−δβσδ4(x 2−y 2)(3.4)which are given by Eqs.(C2)and (D2)respectively with the source J being set to vanish.We note here that the self-energies,as easily proved,are the same as those defined in Eqs.(2.11)and (2.15).Next,we derive the B-S equation satisfied by the Green function G (x 1,x 2;y 1,y 2).For this purpose,we first write down the equation of motion describing variation of the conventional Green function G (x 1,x 2;y 1,y 2)with y 1which is obtained from Eq.(C5)by setting J =0and adding the term related to the self-energy[G (i ←−∂y 1+m 1−Σ)]αβρσ(x 1,x 2;y 1,y 2)=−δαρδ4(x 1−y 1)S c F (x 2−y 2)βσ−C ρσδ4(y 1−y 2)S ∗F (x 1−x 2)αβ+G a µ(y 1|x 1,x 2;y 1,y 2)αβτσ(Γaµ)τρ− d 4z 1G (x 1,x 2;z 1,y 2)αβτσΣ(z 1,y 1)τρ(3.5)where G a µ(y 1|x 1,x 2;y 1,y 2)is the Green function with a gluon field at y 1in it whose expression can be read from Eq.(2.22).Substituting in Eq.(3.5)the relation given in Eq.(2.4)and the following relation which follows from Eq.(2.23)G a µ(y i |x 1,x 2;y 1,y 2)αβρσ=G a µ(y i |x 1,x 2;y 1,y 2)αβρσ+S ∗F (x 1−x 2)αβS ∗F (i ←−∂y 1+m 1−Σ)]ρσ(y 1,y 2)=C ρσδ4(y 1−y 2)(3.7)which is given by Eqs.(C8)-(C10),it can be found[G (i ←−∂y 1+m 1−Σ)]αβρσ(x 1,x 2;y 1,y 2)=−δαρδ4(x 1−y 1)S c F (x 2−y 2)βσ+G a µ(y 1|x 1,x 2;y 1,y 2)αβτσ(Γaµ)τρ− d 4z 1G (x 1,x 2;z 1,y 2)αβτσΣ(z 1,y 1)σρ.(3.8)In order to derive the B-S equation,we need to operate on the both sides of the above equation with the operator (i ←−∂y 2+m 2−Σc ),[G (i ←−∂y 1+m 1−Σ)(i ←−∂y 2+m 2−Σc )]αβρσ(x 1,x 2;y 1,y 2)=δαρδβσδ4(x 1−y 1)δ4(x 2−y 2)+[G a µ(i ←−∂y 2+m 2−Σc )]αβτσ(y 1|x 1,x 2;y 1,y 2)(Γaµ)τρ− d 4z 1[G (i ←−∂y 2+m 2−Σc )]αβτσ(x 1,x 2;z 1,y 2)Σ(z 1,y 1)τρ(3.9)where Eq.(3.4)has been used.For computing the third term in the equation,we start from the equation of motion which is obtained from Eq.(D8)with setting J =0and supplementing the self-energy-related term[G (i ←−∂y 2+m 2−Σc )]αβρσ(x 1,x 2;y 1,y 2)=−δβσδ4(x 2−y 2)S F (x 1−y 1)αρ−C ρσδ4(y 1−y 2)S ∗F (x 1−x 2)αβ+G b ν(y 2|x 1,x 2;y 1,y 2)αβρδ(S ∗F (i ←−∂y 2+m 2−Σc )]ρσ(y 1,y 2)=C ρσδ4(y 1−y 2)(3.11)which is given by Eqs.(D14)-(D16)and the relations represented in Eq.(2.15),one can get such an equation that[G (i ←−∂y 2+m 2−Σc )]αβρσ(x 1,x 2;y 1,y 2)=−δβσδ4(x 2−y 2)S F (x 1−y 1)αρ+G b ν(y 2|x 1,x 2;y 1,y 2)αβρδ(Λ∗a µ(i ←−∂y 2+m 2−Σc )]ρσ(y 1|y 1,y 2).(3.13)The first term can be calculated by virtue of the equation of motion derived in Eq.(D9).With addition of the self-energy-relevant term to Eq.(D9),we have[G aµ(i ←−∂y2+m2−Σc)]αβρσ(y1|x1,x2;y1,y2)=−δβσδ4(x2−y2)Λaµ(y1|x1,y1)αρ−Cρσδ4(y1−y2)Λ∗aµ(y1|x1,x2)αβ+G abµν(y1,y2|x1,x2;y1,y2)αβρδ(Λ∗ab µν(y1,y2|y1,y2)ρσ(3.15)whereΓbν)δσ− d4z2G aµ(y1|x1,x2;y1,z2)αβρδΣc(z2,y2)δσ−S∗F(x1−x2)αβΓbν)δσ+S∗F(x1−x2)αβ d4z2Λ∗aµ(i ←−∂y2+m2−Σc)]ρσ(y1|y1,y2)=Γbν)δσ− d4z2Γbν)δσ− d4z2G aµ(y1|x1,x2;y1,z2)αβρδΣc(z2,y2)δσ.(3.18) Substitution of Eqs.(3.12)and(3.18)in Eq.(3.9)yields[G(i ←−∂y1+m1−Σ)(i←−∂y2+m2−Σc)]αβρσ(x1,x2;y1,y2)=δαρδβσδ4(x1−y1)δ4(x2−y2)+H2(x1,x2;y1,y2)αβρσ(3.19) whereH2(x1,x2;y1,y2)αβρσ=5j=1H(j)2(x1,x2;y1,y2)αβρσ(3.20)in whichH(1)2(x1,x2;y1,y2)αβρσ=− d4z2G aµ(y1|x1,x2;y1,z2)αβτδΣc(z2,y2)δσ(Γaµ)τρ,(3.21)H(2)2(x1,x2;y1,y2)αβρσ=− d4z1G bν(y2|x1,x2;z1,y2)αβτδΣ(z1,y1)τρ(Γbν)δσ,(3.23)H(4)2(x1,x2;y1,y2)αβρσ=δ4(y1−y2)Λ∗aµ(y1|x1,x2)αβ(CΓaµ)σρ(3.24) andH(5)2(x1,x2;y1,y2)αβρσ= d4z1d4z2G(x1,x2;z1,z2)αβτδΣ(z1,y1)τρΣc(z2,y2)δσ.(3.25) By applying the B-S equation given in Eq.(3.19),Eq.(3.1)can be written asK(x1,x2;y1,y2)αβρσ=Q(x1,x2;y1,y2)αβρσ− d4z1d4z2K(x1,x2;z1,z2)αβτδH2(z1,z2;y1,y2)τδρσ.(3.26) To reach a closed expression of the B-S kernel,it is necessary to eliminate the kernel appearing in the second term on the RHS of Eq.(3.26).For this purpose,we operate on the both sides of Eq.(2.41)with the inverse of the Green function G(x1,x2;y1,y2).With this operation,noticingd4z1d4z2G(x1,x2;z1,z2)αβγλG−1(z1,z2;y1,y2)γλρσ=δαρδβσδ4(x1−y1)δ4(x2−y2),(3.27) one getsK(x1,x2;z1,z2)αβτδ= d4u1d4u2H1(x1,x2;u1,u2)αβγλG−1(u1,u2;z1,z2)γλτδ.(3.28) Upon inserting the above expression into Eq.(3.26),wefinally arrive atK(x1,x2;y1,y2)αβρσ=Q(x1,x2;y1,y2)αβρσ−S(x1,x2;y1,y2)αβρσ(3.29) whereS(x1,x2;y1,y2)αβρσ= d4u1d4u2d4v1d4v2H1(x1,x2;u1,u2)αβγλG−1(u1,u2;v1,v2)γλτδH2(v1,v2;y1,y2)τδρσ.(3.30) As we see,the B-S kernel shown above contains two terms.The second term has been explicitly written out.It contains a few types of the Green functions as well as the self-energies appearing in the mutually conjugate functions H1(x1,x2;y1,y2)and H2(x1,x2;y1,y2)shown in Eqs.(2.35)-(2.40)and(3.20)-(3.25)respectively.Clearly,to give afinal expression of the B-S kernel,according to the definition in Eq.(3.2),we need to calculate the function Q(x1,x2;y1,y2)by means of the B-S equations with respect to y1and y2for the Green functions involved in the function H1(x1,x2;y1,y2).We leave the calculations in the next section.IV.CLOSED EXPRESSION OF THE B-S KERNELThis section is used to calculate the function Q(x1,x2;y1,y2)so as to give thefinal expression of the B-S kernel. In accordance with the expressions shown in Eqs.(3.2)and(2.35),we can writeQ(x1,x2;y1,y2)αβρσ=5i=1Q i(x1,x2;y1,y2)αβρσ(4.1)whereQ i(x1,x2;y1,y2)αβρσ=[H(i)1(i ←−∂y1+m1−Σ)(i←−∂y2+m2−Σc)]αβρσ(x1,x2;y1,y2).(4.2)This expression indicates that to compute each Q i(x1,x2;y1,y2),we need to derive the B-S equations with respect to y1and y2for the Green functions contained in the function H1(x1,x2;y1,y2).We will separately calculate each Q i(x1,x2;y1,y2)below.a.Calculation of Q1(x1,x2;y1,y2)Based on Eqs.(4.2)and(2.36),we can writeQ1(x1,x2;y1,y2)αβρσ=−(Γaµ)αγ d4u2Σc(x2,u2)βλ[G aµ(i←−∂y1+m1−Σ)(i←−∂y2+m2−Σc)]γλρσ(x1|x1,u2;y1,y2).(4.3) To calculate the above function,it is necessary to start from the following equation of motion which is established from Eq.(C6)by setting the source J=0,G aµ(x1|x1,u2;y1,y2)γλτσ(i ←−∂y1+m1)τρ=−δγρδ4(x1−y1)Λc aµ(x1|u2,y2)λσ−Cρσδ4(y1−y2)Λ∗aµ(x1|x1,u2)γλ+G abµν(x1;y1|x1,u2;y1,y2)γλτσ(Γaµ)τρ(4.4)where the Green functions have been represented respectively in Eqs.(2.19),(2.20)and(2.22).Considering the definitions given in Eq.(2.26)and in the followingG abµν(x i;y j|x1,u2;y1,y2)γλρσ=G abµν(x i;y j|x1,u2;y1,y2)γλρσ+Λ∗aµ(x i|x1,u2)γλΓbν)δσ− d4v2Λcaµ(x1|u2,v2)λδΣc(v2,y2)δσ(4.8) where the two Green functions were represented in Eq.(2.19).The third term in Eq.(4.7)can be calculated by virtue of the equation given in Eq.(D10)G aµ(x1|x1,u2;v1,y2)γλτδ(i ←−∂y2+m2)δσ=−δλσδ4(u2−y2)Λaµ(x1|x1,v1)γτ−Cτσδ4(v1−y2)Λ∗aµ(x1|x1,u2)γλ+G abµν(x1;y2|x1,u2;v1,y2)γλτδ(Γbν)δσ− d4v2G aµ(x1|x1,u2;v1,v2)γλτδΣc(v2,y2)δσ.(4.10) For calculating the second term in Eq.(4.7),it is needed to use the following equation obtained from Eq.(D11)by setting J=0[G abµν(i ←−∂y2+m2)]γλτσ(x1;y1|x1,u2;y1,y2)γλτσ=−δλσδ4(u2−y2)Λabµν(x1;y1|x1,y1)γτ−Cτσδ4(y1−y2)Λ∗abµν(x1;y1|x1,u2)γλ+G abcµνκ(x1;y1,y2|x1,u2;y1,y2)γλτδ(Λ∗bcνκ(y1,y2|y1,y2)τσ(4.12)which is implied by Eq.(2.23)and utilizing Eqs.(4.11)and(3.17),an equation of motion for the Green function G abµν(x1;y1|x1,u2;y1,y2)will be found to be[G abµν(i ←−∂y2+m2−Σc)]γλτσ(x1;y1|x1,u2;y1,y2)γλτσ=−δλσδ4(u2−y2)Λabµν(x1;y1|x1,y1)γτ−Cτσδ4(y1−y2)Λ∗abµν(x1;y1|x1,u2)γλ+G abcµνκ(x1;y1,y2|x1,u2;y1,y2)γλτδ(When Eqs.(4.8),(4.10)and(4.13)are inserted into Eq.(4.7)and then Eq.(4.7)is inserted into Eq.(4.3),an explicit expression of the function Q1(x1,x2;y1,y2)will be derived as given in the followingQ1(x1,x2;y1,y2)αβρσ=R1(x1,x2;y1,y2)αβρσ+M1(x1,x2;y1,y2)αβρσ+ d4v1d4v2H(1)1(x1,x2;v1,v2)αβτδΣ(v1,y1)τρΣc(v2,y2)δσ(4.14) whereR1(x1,x2;y1,y2)αβρσ=δ4(x1−y1)(Γaµ)αρ d4u2Σc(x2,u2)βλ[Λc abµν(x1;y2|u2,y2)λδ(Γcκ)δσ− d4v2G abµν(x1;y1|x1,u2;y1,v2)γλτδΣc(v2,y2)δσ(Γbν)τρ− d4v1G abµν(x1;y2|x1,u2;v1,y2)γλτδΣ(v1,y1)τρ(Γaµ)βλ d4u1Σ(x1,u1)αγ[G aµ(i←−∂y1+m1−Σ)(i←−∂y2+m2−Σc)]γλρσ(x2|u1,x2;y1,y2)(4.17) In comparison of the above expression with that denoted in Eq.(4.3),it is clearly seen that the function Q2(x1,x2;y1,y2)αβρσcan explicitly be written out from the expression of Q1(x1,x2;y1,y2)αβρσshown in Eqs.(4.14)-(4.16)by the following replacements:(Γaµ)αγ d4u2Σc(x2,u2)βλ→(Γaµ)βσ d4u1Σ(x1,u1)αγ[Λabµν(x2;y1|u1,y1)γτ(Γbν)τρ− d4v1Λaµ(x2|u1,v1)γτΣ(v1,y1)τρ]+Σ(x1,y1)αρ(Γbν)δσ− d4v2Λc aµ(x2|x2,v2)λδΣc(v2,y2)δσ]−δ4(y1−y2)(Γaµ)βλ d4u1Σ(x1,u1)αγ[G abcµνκ(x2;y1,y2|u1,x2;y1,y2)γλτδ(Γbν)τρ((4.20)Γbν)δσ]and the function H(2)1(x1,x2;v1,v2)was defined in Eq.(2.37).c.Calculation of Q3(x1,x2;y1,y2)In accordance with Eqs.(4.2)and(2.38),the function Q3(x1,x2;y1,y2)is known to beQ3(x1,x2;y1,y2)αβρσ=(Γaµ)αγ(G abµν(x1,x2|x1,x2;y1,y2)γλτσ(i ←−∂y1+m1)τρ=−δγρδ4(x1−y1)Λc abµν(x1,x2|x2,y2)λσ−Cρσδ4(y1−y2)Λ∗abµν(x1,x2|x1,x2)γλ+G abcµνκ(x1,x2;y1|x1,x2;y1,y2)γλτσ(Γcκ)τρ(4.22)where the Green functions were respectively represented in Eqs.(2.19),(2.20)and(2.22).Grounded on the definition given in Eqs.(2.31)and the following one which can be written out from Eq.(2.23):G abc µνκ(x1,x2,y i|x1,x2;y1,y2)γλτσ=G abcµνκ(x1,x2,y i|x1,x2;y1,y2)γλτσ+Λ∗abµν(x1,x2|x1,x2)γλΓcκ)δσ− d4v2Λc abµν(x1,x2|x2,v2)λδΣc(v2−y2)δσ(4.26) wherei∆abµν(x1−x2)= 0+ T[A aµ(x1)A bν(x2)] 0− (4.27) is the gluon propagator and the other Green functions were defined in Eq.(2.19).The third term in Eq.(4.25)will be evaluated with the aid of the equation given by Eq.(D12)G abµν(x1,x2|x1,x2;v1,y2)γλτδ(i ←−∂y2+m2)δσ=−δλσδ4(x2−y2)Λabµν(x1,x2|x1,v1)γτ−Cτσδ4(v1−y2)Λ∗abµν(x1,x2|x1,x2)γλ+G abcµνκ(x1,x2;y2|x1,x2;v1,y2)γλτδ(Γcκ)δσ− d4v2G abµν(x1,x2|x1,x2;v1,v2)γλτδΣc(v2,y2)δσ.(4.29)The second term in Eq.(4.25)can be calculated by means of the equation derived in Eq.(D13)G abcµνκ(x1,x2;y1|x1,x2;y1,y2)γλτδ(i←−∂y2+m2)δσ=−δλσδ4(x2−y2)Λabcµνκ(x1,x2;y1|x1,y1)γτ−Cτσδ4(y1−y2)Λ∗abcµνκ(x1,x2;y1|x1,x2)γλ+G abcdµνκθ(x1,x2;y1,y2|x1,x2;y1,y2)γλτδ(Λ∗cdκθ(y1,y2|y1,y2)τσ(4.31)which follows from Eq.(2.23)and applying the equations in Eqs.(4.30)and(3.17),it is easy tofind[G abcµνκ(i←−∂y2+m2−Σc)]γλτσ(x1,x2;y1|x1,x2;y1,y2)=−δλσδ4(x2−y2)Λabcµνκ(x1,x2;y1|x1,y1)γτ−Cτσδ4(y1−y2)Λ∗abcµνκ(x1,x2;y1|x1,x2)γλ+G abcdµνκθ(x1,x2;y1,y2|x1,x2;y1,y2)γλτδ(Upon substituting Eqs.(4.26),(4.29)and(4.32)in Eq.(4.25)and then inserting Eq.(4.25)into Eq.(4.21),we eventually arrive atQ3(x1,x2;y1,y2)αβρσ=K(0)t(x1,x2;y1,y2)αβρσ+Γaν)βσi∆abµν(x1−x2)(4.34) which is the t-channel one-gluon exchange kernel,Γaν)βλG abcdµνκθ(x1,x2;y1,y2|x1,x2;y1,y2)γλτδ(Γcκ)τρ(Γaν)βλ[Λc abcµνκ(x1,x2;y2|x2,y2)λδ(Γbν)βσ((Γaµ)αγ[Λabcµνκ(x1,x2;y1|x1,y1)γτ(Γcκ)τρ− d4v1Λabµν(x1,x2|x1,v1)γτΣ(v1,y1)τρ]+δ4(y1−y2)(Γaµ)αγ(Γaν)βλ[ d4v2G abcµνκ(x1,x2;y1|x1,x2;y1,v2)γλτδΣc(v2,y2)δσ(Γcκ)τρ+ d4v1G abcµνκ(x1,x2;y2|x1,x2;v1,y2)γλτδΣ(v1,y1)τρ(ΓaµC)βα[Λ∗aµ(i ←−∂y1+m1−Σ)]ρσ(x2|y1,y2)=Λ∗aµ(x2|v1,y2)τσΣ(v1,y1)τρ(4.39)where the Green functions was written in Eq.(2.21). Now,let us operate on Eq.(4.39)with the operator(i ←−∂y2+m2−Σc),[Λ∗ab µν(i←−∂y2+m2−Σc)]τσ(x2;y1|y1,y2)(Γbν)τρ− d4v1[Λ∗aµ(i ←−∂y2+m2−Σc)]τσ(x2|v1,y2)=Γbν)δσ− d4v2Λ∗ab µν(i←−∂y2+m2−Σc)]τσ(x2,y1|y1,y2)=Cτσδ4(y1−y2)i∆abµν(x2−y1)+Γcκ)δσ− d4v2Substituting atfirst Eqs.(4.41)and(4.42)into Eq.(4.40)and then Eq.(4.40)into Eq.(4.38),the function Q4(x1,x2;y1,y2)will be explicitly written in the formQ4(x1,x2;y1,y2)αβρσ=K(0)s(x1,x2;y1,y2)αβρσ+R4(x1,x2;y1,y2)αβρσ+ d4v1d4v2H(4)1(x1,x2;v1,v2)αβτδΣ(v1,y1)τρΣc(v2,y2)(4.43) whereK(0)s(x1,x2;y1,y2)αβρσ=δ4(x1−x2)δ4(y1−y2)(ΓaµC)βα{[Γcκ)δσ− d4v2Λ∗abµν(x2;y2|v1,y2)τδΣ(v1,y1)τρ(q annihilation and creation process which takes place between the quark(antiquark)in the initial state and the antiquark(quark)in thefinal state as indicated by the gluon propagator in Eq.(4.44),not between the quark and the antiquark both of which belong to the initial state or thefinal state B-S amplitude for a bound state.e.Calculation of Q5(x1,x2;y1,y2)From Eqs.(4.2)and(2.40),we haveQ5(x1,x2;y1,y2)αβρσ= d4u1d4u2Σ(x1,u1)αγΣc(x2,u2)βλ[G(i←−∂y1+m1−Σ)(i←−∂y2+m2−Σc)]γλρσ(u1,u2;y1,y2).(4.46) By applying the equation given in Eq.(3.19),the above function can explicitly be represented asQ5(x1,x2;y1,y2)αβρσ=R0(x1,x2;y1,y2)αβρσ+ d4u1d4u2Σ(x1,u1)αγΣc(x2,u2)βλH2(u1,u2;y1,y2)γλρσ(4.47) whereR0(x1,x2;y1,y2)αβρσ=Σ(x1,y1)αρΣc(x2,y2)βσ(4.48) and H2(u1,u2;y1,y2)γλρσwas shown in Eqs.(3.20)-(3.25).In summary,combining the expressions given in Eqs.(4.14),(4.18),(4.33),(4.43)and(4.47),an explicit expression of the function Q(x1,x2;y1,y2)written in Eq.(4.1)will be eventually found as shown in the followingQ(x1,x2;y1,y2)αβρσ=K(0)t(x1,x2;y1,y2)αβρσ+K(0)s(x1,x2;y1,y2)αβρσ+here j=1,2and all the functions on the RHS of Eqs.(4.50)-(4.52)have already been explicitly given before.Now let us turn to the function S(x1,x2;y1,y2)αβρσexpressed in Eq.(3.30).According to the definitions denoted in Eqs.(2.35),(3.20)and(4.52),we can writeH j(x1,x2;y1,y2)αβρσ=H j(x1,x2;y1,y2)αβρσ+H(5)j(x1,x2;y1,y2)αβρσ(4.53) .Thus,Eq.(3.30)can be rewritten in the formS(x1,x2;y1,y2)αβρσ= d4u1d4u2d4v1d4v2H1(x1,x2;u1,u2)αβγλG−1(u1,u2;v1,v2)γλτδH2(v1,v2;y1,y2)τδρσ+ d4u1d4u2d4v1d4v2H(5)1(x1,x2;u1,u2)αβγλG−1(u1,u2;v1,v2)γλτδH2(v1,v2;y1,y2)τδρσ+ d4u1d4u2d4v1d4v2H1(x1,x2;u1,u2)αβγλG−1(u1,u2;v1,v2)γλτδH(5)2(v1,v2;y1,y2)τδρσ.(4.54)When the functions H(5)1(x1,x2;u1,u2)αβγλand H(5)2(v1,v2;y1,y2)τδρσin the second and third terms are respectively replaced by the expressions given in Eqs.(2.40)and(3.25)and utilizing the relation in Eq.(3.27),it is easy to see that the last two terms in Eq.(4.54)exactly equal to the last two terms in Eq.(4.49)respectively.Therefore,when we substitute Eqs.(4.49)and(4.54)into Eq.(3.29),the above-mentioned terms are cancelled with each other.Thus, the B-S kernel will befinally expressed byK(x1,x2;y1,y2)αβρσ=Q(x1,x2;y1,y2)αβρσ−S(x1,x2;y1,y2)αβρσ(4.55) whereQ(x1,x2;y1,y2)αβρσ=K(0)t(x1,x2;y1,y2)αβρσ+K(0)s(x1,x2;y1,y2)αβρσ+q Green functions and given a closed and explicit expression shown in Eqs.(4.55)-(4.57).This expression is manifestly Lorentz-covariant even in the space-like region of Minkowski space where the bound states exist and it suits to not only the case that the quark and antiquark have differentflavors,but also the case where they have the sameflavor. In the latter case,the masses of the quark and antiquark are the same,m1=m2=m.Meanwhile,the B-S kernel contains the part describing the qΛ∗a...b...µ...ν...(x i...,y j,...|y1,y2)which give the higher order perturbative corrections to the vertices of the s-channel one-gluon exchange kernel.It is well known that the s-channel one-gluon exchange kernel gives no contribution to the q q color singlet.But, this does not imply that the qq annihilation part of the kernel is absent.In this case,the B-S kernel is of a simpler expression which can be written out from the corresponding expression given in the preceding section by deleting out the q。

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新视野大学英语_第二版_第三册课后习题答案(完整版)

新视野大学英语_第二版_第三册课后习题答案(完整版)

新视野第三册答案Unit 1Section A. The Expensive Fantasy of Lord Williams《读写教程III》:Ex. II, p. 91.Because this is a title bought with stolen money. The guy‘s real name is Anthony Williams.2.It‘s small, with a population of only 320.3.No. He looks like a Scottish noble, soft-spoken and wealthy.4.The truth is that the man with endless money and a friendly manner was not a lord at all but agovernment employee living out a fantasy that he was a Scottish noble and paying for it by stealing funds from Scottish Yard.5.He stole more than eight million pounds over eight years and poured about five millionpounds into the village.6.Most of the stolen money was supposed to be used to pay spies and conduct secret activitiesagainst the Irish Republican Army.7.He used the money to buy an estate, a beautiful home, and a dozen noble titles. But most of all,he sunk his dishonest gains into the village, buying multiple cottages, a pub and a run-down hotel and turning them into very good-looking places.8.His bank deposits were so large that they were noticed by the bank‘s management. The bankthen notified the police, who discovered that the criminal was one of their own.9.Because in the eyes of some villagers Williams is a helper, pouring most of his stolen moneyinto the village and giving jobs to 43 people.10.He said in an interview after he was arrested: ―I discovered this bloody huge amount of money.I went from the need to pay off a few debts to what can only be described as greed. There isno way to justify it.‖《读写教程Ⅲ》:Ex. Ⅲ, p. 91.suspicion2.restored3.considerate4.inherited5.furnish6.justify7.substantial8.fantastic1.To his embarrassment he discovered2.like that3.strike deals with4.live it out5.falls upon dark days6.nothing but7.captured the heart of the little boy with8.raise a glass to《读写教程Ⅲ》: Ex. Ⅴ, p. 101.economy2.business3.campaign4.poll5.survey6.research7.lessons8.study《读写教程III》: Ex. VI, p. 111.well-advised (明智的)2.narrow-minded (心胸狭窄的)3.wide-eyed (眼睛睁大的)4.soft-spoken (说话温和的)5.big-headed (妄自尊大的)6.single-minded (专心致志的)7.well-meant (用意良好的)8.quick-tempered (易怒的)《读写教程III》: Ex. VII, p. 111.air-conditioned2.handmade3.thunder-struck4.heart-felt5.data-based6.self-employed7.custom-built8.weather-beaten1.Well-meant as it was, the decision spoiled the peace talk in the Middle East.2.Hard as he tried, he failed to deceive the police commissioner in London in the end.3.Poor as he was, she gave up the idea to marry him.4.Friendly as he may seem, I won‘t regard him as considerate.5.Suspicious as she was of him, she never came to the idea that the wealthy, soft-spoken,well-mannered man was a criminal.《读写教程Ⅲ》: Ex. Ⅸ., p. 121.Now (that) you have studied the above models and understood the meaning and usage of theexpression ―now that‖, you know how to do the following exercises.2.Now (that) I‘ve heard the music, I understand why you like it.3.Now that the hotel is beautifully restored, many travelers like to stay in it.4.Now that the criminal turned out to be one of their own, the London police commissionerpublicly apologized for poorly supervising his department.5.Now that you have got an MA degree, you are qualified for a PhD program.《读写教程Ⅲ》: Ex. Ⅹ, p. 131.My thanks go to those who still stuck by me when I fell upon dark days.2.Now that he has published a popular novel which earns him a large amount of money, he isable to buy a new house and a car.3.The police said that their suspicions were aroused because the girl had other marks on herbody.4.How can you talk to her like that? She is the one who brought you up and helped you finishschool.5.Hard as the road for these students after school will be, their prospects are bright.6.In order to have enough money to run the business, he sold his newly-bought house at auctioneven at a substantial loss.7.He is fully justified in criticizing the police commissioner for poorly supervising hisdepartment.8.These ancient buildings which are under protection have been restored beautifully to attractforeigners.《读写教程III》: Ex. XI, p. 131.周六晚，在―牢骚酒吧‖，村民依旧乐意向―威廉斯勋爵‖祝酒，尽管这个头衔现在只能引来阵阵笑声。

2005-2006学年春季学期大学英语跨文化交际课程期末试题...

2005-2006学年春季学期大学英语跨文化交际课程期末试题...

黑龙江大学 2005-2006 学年春季学期大学英语跨文化交际课程期末试题
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2005-2006 学年春季学期大学英语跨文化交际课程期末试题（B 卷） 学年春季学期大学英语跨文化交际课程期末试题（
订 线 题 号 I 40 分 II 15 分 III 15 分 IV 20 分 V 10 分 （院系： 院系： 专业： 专业： 卷 面 分 100 随 堂 测 试 20 分 课 堂 表 现 10 分 年级： 年级： 评 卷 人 ）
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评卷人
Part I. Choose one word or expression from those in the box below to fill the gap in each of the sentences. Write the correct letters in the blanks on your answer sheet. （2×20=40） ） c. Communication competence j. Symbols
1. Assume that global warming is a fact, and, as a result, assume that summers in the United States average 43℃ (109℉). It would be logical to make adjustments: Rather than air condition building all day, you might close schools and businesses in the afternoons to conserve energy. Such adjustments would make sense. Why then do some people attribute sensible midday siestas in hot climates to laziness? 2 An international student in a U.S. grocery may be asked, “paper or plastic?” The student knows what paper is and what plastic is, but don’t understand the question.
《英语教学法教程》（王蔷）考研复习资料

《英语教学法教程》（王蔷）考研复习资料

n1. The ultimate goal of ELT: the ultimate of foreign language teaching is to enable students to usethe foreign language in work or life when necessary. Thus we should teach that part of the language that will be used (rather than all part of the language).Definition of task: a piece of classroom work which involves learners in comprehending, manipulating, producing or interacting in the target language while their attention in principally focused on meaning rather than form. (Nunan 1989:8)A lesson plan is a framework of a lesson in which teachers make advance decision about what they hope to achieve and how they would like to achieve it. In other words, teachers need to think about the aims to be achieved, materials to be covered, activities to be organized, and techniques and resources to be used in order to achieve the aims of the lesson.Classroom management is the way teachers organize what goes on in the classroom. It contributes directly to the efficiency of teaching and learning as the most effective activities can be made almost useless if the teacher does not organize them efficiently. As the goal of classroom management is to create an atmosphere conductive to interacting in English in meaningful ways.Deductive method: The Deductive method relies on reasoning, analyzing and comparing. First, the T writes an example on board or draws attention to an example in the textbook. Second, the T explains the underlying rules regarding the forms and positions of certain structural words. The explanations are often done in the S’s native language and use grammatical terms. Sometimes, comparisons are made between the native language and the target language or between the newly presented structure and previously learned structures. Finally, the Ss practice applying the rule to produce sentences with given prompts.Inductive method: the T provides learners with authentic language data and induces the learners to realize grammar rules without any forms of explicit explanation.1. Language:” Language is a system of arbitrary vocal symbols used for human communication.” It can be understood in the following six aspects:Language as system;Language as symbolic;Language as arbitrary;Language as vocal;Language as human;Language as communicationBottom-up modelSome teachers teach reading by introducing new vocabulary and new structures first and then going over the text sentence by sentence. This way of teaching reading reflects the belief thatreading comprehension is based on the understanding and mastery熟练of all the new words, new phrases, and new structures as well as a lot of reading aloud practice. Also, this reading follows a linear process from the recognition of letters, to words, to phrases, to sentences, toparagraphs, and then to the meaning of the whole text. This way of teaching reading is said to follow a bottom-up model.2). Top-down modelIt is believed that in teaching reading, the teacher should teach the background knowledge firstso that students equipped with such knowledge will be able to guess meaning from the printed page. This process of reading is said to follow the top-down model of teaching reading just as Goodman(1970) once said that reading was “a psycholinguistic guessing game”2. Structural view:The structural view sees language as a linguistic system made up of various subsystems: fromphonological, morphological, lexical, etc. to sentences.3. The functional view:The functional view sees language as a linguistic system but also as a means for doing things.Most of our day-to-day language use involves functional activities: greetings; offering,suggesting, advising, apologizing, etc.The communicative view of languageThe communicative, or functional view of language is the view that language is a vehiclefor the expression of functional meaning. The semantic and communicative dimensionsof language are more emphasized than the grammatical characteristics, although theseare also included.4. The interactional view:The interactional view considers language as a communicative tool, whose main use is to buildup and maintain social relations between people.1) The behaviorist theory( Skinne r)-- a stimulus-response theory of psychologyThe key point of the theory of conditioning is that "you can train an animal to do anything(within reason) if you follow a certain procedure which has three major stages, stimulus,response, and reinforcement"2) Cognitive theory( Noam Chomsky):The term cognitive is to describe loosely methods in which students are asked to thinkrather than simply repeat.The goal of CLTThe goal of CLT is to develop students' communicative competenceLesson planning means making decisions in advance about what techniques, activities andmaterials will be used in the class.Teaching stages and procedures:Teaching stages are the major steps that language teachers go through in the classroom.Procedures are the detailed steps in each teaching stage.31. Three P's model: presentation, practice and production.SkimmingSkimming means reading quickly to get the gist, i.e. the main idea of the text.ScanningScanning means to read to locate/get specific information.1). DiscussionA discussion is often used for a) exchange of personal opinions. This sort of discussion canstart with a question like "What do you think of?"b) stating of personal opinions ongeneral issues. c) problem-solving.d) the ranking(分类；顺序)of alternatives e) deciding upon priorities(先;前)etc.2). Role-playRole-play is a very common language learning activity where students play differentroles and interact from the point of view of the roles they play.What’s called A process approach to writing1). DefinitionWhat really matters or makes a difference is the help that the teacher provides toguide the students through the process that they undergo when they are writing. What’s the assessmentAssessment in ELT means to discover what the learners know and can do at a certain stage of the learning process.a. Grammar Translation:The Grammar Translation method started around the time of Erasmus (1466-1536). Its primary focus is on memorization of verb paradigms, grammar rules, and vocabulary. Application of this knowledge was directed on translation of literary texts--focusing of developing students' appreciation of the target language's literature as well as teaching the language. Activities utilized in today's classrooms include: questions that follow a reading passage; translating literary passages from one language to another; memorizing grammar rules; memorizing native-language equivalents of target language vocabulary. (Highly structured class work with the teacher controlling all activities.)b. Direct Method:The Direct Method was introduced by the German educator Wilhelm Viëtor in the early 1800's.Focusing on oral language, it requires that all instruction be conducted in the target language with no recourse to translation. Reading and writing are taught from the beginning, although speaking and listening skills are emphasized--grammar is learned inductively. It has a balanced, four-skill emphasis.c. The Silent Way:The teacher is active in setting up classroom situations while the students do most of the talkingand interaction among themselves. All four skills (listening, speaking, reading & writing) are taught from the beginning. Student errors are expected as a normal part of learning; theteacher's silence helps to foster self-reliance and student initiative.d. Community Language Learning:Teachers recognize that learning can be threatening and by understanding and acceptingstudents' fears, they help their students feel secure and overcome their fears of languagelearning--ultimately providing students with positive energy directed at language learning. Students choose what they want to learn in the class and the syllabus is learner-generated.e. Natural Approach:Introduced by Gottlieb Henese and Dr. L. Sauveur in Boston around 1866. The NaturalApproach is similar to the Direct Method, concentrating on active demonstrations to convey meaning by associating words and phrases with objects and actions. Associations are achieved via mime, paraphrase and the use of manipulatives. Terrell (1977) focused on the principles of meaningful communication, comprehension before production, and indirect error correction. Krashen's (1980) input hypothesis is applied in the Naturale. Reading Method:The reading method was prominent in the U.S. following the Committee of Twelve in 1900 andfollowing the Modern Foreign Language Study in 1928. The earlier method was similar to thetraditional Grammar/Translation method and emphasized the transference of linguistic understanding to English. Presently, the reading method focuses more on silent reading for comprehension purposes.f. ASTP and the Audiolingual Method:This approach is based on the behaviorist belief that language learning is the acquisition of a setof correct language habits. The learner repeats patterns and phrases in the language laboratoryuntil able to reproduce them spontaneously.ASTP (Army Specialized Training Program) was an intensive, specialized approach to language instruction used in during the 1940's. In the postwar years, the civilian version of ASTP and the audiolingual method featured memorization of dialogues, pattern drills, and emphasis on pronunciation.g. Cognitive Methods:Cognitive methods of language teaching are based on meaningful acquisition of grammar structures followed by meaningful practice.h. Communicative Methods:The goal of communicative language approaches is to create a realistic context for languageacquisition in the classroom. The focus is on functional language usage and the ability tolearners to express their own ideas, feelings, attitudes, desires and needs. Open endedquestioning and problem-solving activities and exchanges of personal information are utilized as the primary means of communication. Students usually work with authentic materials (authentic realia) in small groups on communication activities, during which they receive practice in negotiating meaning.i. Total Physical Response Method:This approach to second language teaching is based on the belief that listening comprehension should be fully developed before any active oralparticipation from students is expected (just as it is with children when theyare learning their native language) .What is the Grammar-Translation Method?The Grammar-Translation Method is designed around grammatical structures.The Functional-Notional ApproachUnlike the Grammar-Translation Method, which is based on the grammar structures, it thinks thata general learner should take part in the language activities, the functions of language involved inthe real and normal life are most important. For example, the learners have to learn how to give directions, buy goods, ask a price, claim ownership of something and so on. It tells that is not just important to know the forms of the language, it is also important to know the functions and situations, so that the learner could practice real-life communication.Communicative CompetenceBoth knowledge about the language and the knowledge about how to use the language incommunicative situation appropriately.Critical Period Hypothesis 关键期假说This hypothesis states that if humans do not learn a foreign language before a certain age ,then due tochanges such as maturation of the brain ,it becomes impossible to learn the foreign language like a nativespeaker.1.Process-oriented theories:强调过程 are concerned with how the mind organizes newinformation such as habit formation, induction, making inference, hypothesis testing and generalization.2.Condition-oriented theories : 强调条件emphasize the nature of the human and physical context in which language learning takes place, such as the number of students, the kind of input learners receives, and the atmosphere.3.Behavioristtheory ,(Skinner and waston raynor)A the key point of the theory of conditioning is the key point of the theory of conditioning is that”that”that” you can train an animal to do anything if you you can train an animal to do anything if you follow a certain procedure which has three major stages, s timulus, response, and reinforcementB the idea of this method is that language is learned by constant repletion and the reinforcement of the teacher. Mistakes were immediately corrected, and correct utterances were immediately praised.4.Cognitive theory:Chomsky)thinks that language is not a form of behavior,it is an intricate rule-based system a nd a large part of language acquisition is the learning of this system.There are a fin ite number of grammatical rules in the system and with knowledge of these an infinite number of sentences can be produced.5.Constructivist theory:(John Dewey)the constructivist theory believes that learning is aproces in which the learner constructs meaning based on his/her own experiences and what he/he r already knows6.Socio-constructivist theory: (Vygotsky) he emphasizes interaction and engagement with the tar get language in a social context based on the concept of get language in a social context based on the concept of ““Zone of Proximal Development ” (ZPD) and scaffolding .。

(完整版)语用学级期末复习思考题

(完整版)语用学级期末复习思考题

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Put the following English terms into Chinese. (1'×10＝10’)所指对象referent所指论Referential theory专有名词 proper name普通名词 common nouns固定的指称记号 rigid designators指称词语deixical items确定性描述语definite descriptions编码时间 coding—time变异性variability表示反复的词语 iterative表述句 constative补救策略redressive strategies不可分离性 non—detachability不确定性indeterminacy不使用补救策略，赤裸裸地公开施行面子威胁行bald on record without redressive actions 阐述类言语行为 representatives承诺类言语行为 commissives指令类言语行为directives表达类言语行为expressives，宣告类言语行为declarations诚意条件 sincerity condition次要言外行为 secondary illocutionary act等级含义 scalar implicature等级划分法 rating scales副语言特征 paralinguistic features非公开施行面子威胁行为 off record非规约性non—conventionality非规约性意义 non-conventional implicature非论证性的 non—demonstrative非自然意义non—natural meaning (meaning—nn)否定测试法negation test符号学 semiotics构成性规则 constitutive rules古典格莱斯会话含义理论 Classical Gricean theory of conversational implicature关联论Relevance Theory关联原则Principle of Relevance归属性用法 attributive use规约性含义conventional implicature人际修辞 interpersonal rhetoric篇章修辞textual rhetoric含蓄动词 implicative verbs合适条件 felicity conditions呼语 vocatives互相显映 mutually manifest会话含义 conversational implicature话语层次策略 utterance-level strategy积极面子positive face间接言语行为 indirect speech acts间接指令 indirect directives结语 upshots交际意图communicative intention可撤销性 cancellability可废弃性 defeasibility可推导性 calculability跨文化语用失误cross—cultural pragmatic failure跨文化语用学cross—cultural pragmatics命题内容条件 propositional content condition面子保全论 Face-saving Theory面子论 Face Theory面子威胁行为 Face Threatening Acts （FTAs）蔑视 flouting明示 ostensive明示－推理模式ostensive—inferential model摹状词理论Descriptions粘合程度 scale of cohesion篇章指示 discourse deixis前提 presupposition前提语 presupposition trigger强加的绝对级别absolute ranking of imposition确定谈话目的 establishing the purpose of the interaction确定言语事件的性质 establishing the nature of the speech event 确定性描述语 definite descriptions认知语用学 cognitive pragmatics上下文 co—text社会语用迁移sociopragmatic transfer社交语用失误 sociopragmatic failure施为句 performative省力原则 the principle of least effort实情动词 factive verbs适从向 direction of fit手势型用法 gestural usage首要言外行为 primary illocutionary act双重或数重语义模糊 pragmatic bivalence/ plurivalence顺应的动态性 dynamics of adaptability顺应性adaptability语境关系的顺应(contextual correlates of adaptability)、语言结构的顺应(structural objects of adaptability)、顺应的动态性（dynamics of adaptability)和顺应过程的意识程度（salience of the adaptation processes）。